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Downloads
Views
Date
Relevance
Potential Scenario
122
views
62
downloads
0
comments
2003-Fay-Graham-Coupled spring equations
Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
spring mass
oscillation
Hooke's Law
coupled springs
periodic
forcing function
phase portrait
Potential Scenario
139
views
79
downloads
0
comments
2003-Fay-Graham-Coupled spring equations
Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
mass
oscillation
spring\
coupled springs
periodic
fporcing
Modeling Scenario
225
views
214
downloads
0
comments
4-050-ResonanceBeats-ModelingScenario
We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.
Spring 2020 workshop
vibration
tuning
driver
resonance
forced vibration
undamped
beats
naturl frequency
Modeling Scenario
319
views
191
downloads
0
comments
3-010-EnergyInSpringMassSystem-ModlingScenario
As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.
energy
mass-spring system
kinetic energy
potential energy
total energy
Free Online Textbook
216
views
55
downloads
0
comments
2016-I-Liang_Chern-Mathematical Modeling_and_Ordinary_Differential_Equations
We let the author's Table of Contents speak for itself.
differential equations
modeling
textbook
Modeling Scenario
398
views
608
downloads
0
comments
1-076-ClimateBifurcation-ModelingScenario
We cover simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations.
energy balance
climate
energy
albedo
Hysteresis
bifurcation
ice-age
greenhouse
balance
Stefan Boltzmann Law
Potential Scenario
112
views
62
downloads
0
comments
2015-Peter_Cumber-Waggling pendulums and visualization in mechanics
This article describes an equation of motion for a waggling pendulum.
resonance
inverted pendulum
mechanics
damped pendulum
Modeling Scenario
298
views
272
downloads
0
comments
1-098-NeuronDetection-ModelingScenario
Students study a linear, first order, one-dimensional ordinary differential equation (ODE) and learn how it can help understand basics of neural dynamics. The modeling framework is known in mathematical neuroscience as ``integrate-and-fire''...
biology
neuroscience
neuron physiology
voltage
integrate and fire
threfhols
coincidence detection
RC circuit
Potential Scenario
122
views
39
downloads
0
comments
2008-Luis_San_Andrés-Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces
Walk through the cases in context of second order linear constant coefficient differential equation with driving function
driving function
viscous
mechanical system
Article or Presentation
185
views
54
downloads
0
comments
2008-Brian_Winkel-Fourier_Series-Optimization_Opportunity
We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.
optimization
discovery
Fourier
Fourier seris
Modeling Scenario
391
views
265
downloads
0
comments
5-076-LanchesterLaws-ModelingScenario
Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
Lanchester's laws
sensitivity analysisanalysis
Potential Scenario
249
views
40
downloads
0
comments
2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.
predator-prey
harvesting
Pontryagin’s maximum principle
bioeconomic
bionomic equilibrium
biotechnical productivity
catch-rate function
optimal equilibrium
Potential Scenario
182
views
55
downloads
0
comments
2000-Idels-Wang-Harvesting Fisheries Management Strategies With Modified Effort Function
This study concludes that a control parameter beta (the magnitude of the effect of the fish population size on the fishing effort function E), changes not only the rate at which the population goes to equilibrium, but also the equilibrium values.
sustainability
fish
Fishing
management
harvest
fisher
strategy
overfishing
Potential Scenario
151
views
83
downloads
0
comments
2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve
Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived.
kinematics
curve design
highway exit
tangential acceleration
Modeling Scenario
644
views
545
downloads
0
comments
1-032-WordPropagation-ModelingScenario
This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.
Google
exponential growth
language
word problems
etymology
Ngram
propagation
Jumbo
Modeling Scenario
400
views
176
downloads
0
comments
7-008-MachineReplacement-ModelingScenario
Students build an integro-differential equation model using a convolution for machine replacement strategies for two different machine failure models.
Probability
replacement number
Laplace transform
industrial engineering
machine
convolution
distributioj
step function
derivative definition
Article or Presentation
184
views
56
downloads
0
comments
2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions
We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.
circuit
Laplace transform
transfer function
mystery circuit
voltage frequency
two loop circuit
Potential Scenario
165
views
69
downloads
0
comments
2011-W_Wood-Squigonometry
The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = (t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
Trigonometric Functions
circle
squigonometry
inverse function
trigonmetry
Potential Scenario
134
views
52
downloads
0
comments
2015-Carl_Lutzer-Using Expected Value to Introduce the Laplace Transform
We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random.
Expected Value
Riemann sum
net change
Potential Scenario
151
views
33
downloads
0
comments
2011-W_Wood-Squigonometry
The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = x(t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
Trigonometry
Trigonometric Functions
parametric equations
circle
sine
cosine
squigonometry
inverse function
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